The tree on the hill is an anomalous plant seen by Towa and the MC, and is notably not seen by Edward[1], who knows that Towa can see something he cannot. It's implied that neither Kaito nor Haru, who both know of the hill's existence, can see the tree either given Towa's reaction to MC, but it is not explicitly confirmed yet. However, Towa considers MC special for being able to see it[2]. It is also implied that the stars visible are anomalous in some way, as the MC states that it is a starless night[3], and is further surprised to see stars when they begin to stargaze[2].
In the English translation, Towa refers to the tree with she/her pronouns, and notes having conversations with the tree. He also mentions that it cries, which is likely the rattling sound heard in it's initial appearance, given that Towa begins to cry whenever he hears it. His level 22 affinity line also mentions the tree crying, and further mentions that the tree has been waiting for a really long time.
Other conversations Towa has include ones about the condition of the tree and the fruits on it. According to Towa, the tree hasn't been feeling well lately, and will die if something does not change. He refers to the ten[4] glowing fruits as its children, and says that they are getting smaller. MC agrees that each fruit looks 'tired and dry', and looks like they could fall at any moment, and refers to the tree trunk as withered. The tree itself emits light, and MC notes it is wilting / dying, which Towa attributes to there not being enough love. He gives it hugs in order to combat this[2].
Partway through Chapter 7, Towa brought us to the hill to show that the yellow fruit has gotten bigger and brighter, noting that it is the only one to do so (specified in the Japanese text using だけ), and expressing a wish to see the others grow as well[5]. However, at the end of Chapter 7, Towa returns and says that the fruit has shrunk once again[6]. Notably, this part only shows six of the ten fruits.
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Footnotes under the cut due to image size.
Organized in ascending order from middle numbers.
Notes and general theory regarding classification numbers are listed under the cut. Re-classifications of Type or Class will be listed in [Brackets].
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The Endless Black Market - B - Destroyed | The Imperial Auction (Type: Anomalous Simulation)
A Small Case of Symbiosis - B - Captured | A-27-62 Sheepdog (Type: Local God - Animal)
The Secret of Yumeyashiki - B - Destroyed | A-36-3411 Hanao Numata (Type: Vengeful Spirit)
Death Sentence - B - Destroyed | A-37-608 - The Executioner (Type: Ghost Possession)
The Loveless Bride - B - Destroyed | A-39-407 Waves of Love (Type: Binding Spirit)
Black Magic Gig - B - Destroyed | A-533-844 - Takamine (Type: Malevolent Spirit)
The Phantom Dragon Palace - B - Destroyed | A-984-114 - Princess Oto (Type: Siren)
The Witch's Offering - A - Lost | A-1000-6 - Kisaragi Station (Type: Kyklos)
The Laponan Royal Family Decapitation - B - Captured | A-1008-4 - Lapona Royal Property (Type: Dullahan)
Web of Delusion - B - Destroyed | A-1200-105 - International Cemetery (Type: Arachne)
The Witch's Offering - A - Lost | A-1429-950 - The Flower Witch (Type: Witch)
A Flower For Your Sin - B - Destroyed | A-1639-372 - A Mother's Wrath (Type: Cursed Doll)
The Dragon Sea Above the Clouds - A - Temporarily Captured | A-1984-2 - Dragon Triangle (Type: Fáfnir)
Villain’s Bane - B - Destroyed | A-2162-4 - Fabricated Shi San Long (Type: Hundun)
The Wandering Streamer - B - Destroyed | A-2412-43 - Takeru (Type: Tulpa)
Forbidden Playmate - C [Previous: D]- Destroyed | A-2977-3 - Darkwick Academy (Type: Barometz)
The Dragon Sea Above the Clouds - A - Temporarily Captured | A-3912-1 - Origin (Type: Rinfone)
The Immortal Inpatient - A - Captured | A-4122-3 - Patient No. 8445 (Type: Artificial Immortal)
Wish Upon A Firefly - Unknown - Lost | A-4278-1 - Origin (Type: Sky King)
Wish Upon A Firefly - B - Destroyed | A-5060-3 - Hotarubi (Type: Kaleidoscope Mask)
The Long-Legs Estate Faith Healer - B - Destroyed | A-5760-27 - Mr. Long-Legs (Type: Faceless)
A Small Case of Symbiosis - B - Captured | A-5822-2 - Father Farm Cat (Type: Cat)
Containment Facility 6 Mass Breakout - A - Captured | A-6000-1 - Origin (Type: Yoshitaka)
The Laponan Royal Family Decapitation - C - Captured | A-6015-7 - Lapona Royal Property (Category: Mirror of Melancholy)
Rondo der gezeichneten Seelen - C - Captured | A-6505-1 - Origin (Type: The Town Musicians of Bremen)
B - Captured | A-6622-1 - Veil (Type: Hera's Snakes)
Viral Madness - B - Captured | A-6791-12 - National Museum Outbreak (Type: Oui, C’est Bon)
The Oblivion Junket Case - A - Destroyed | A-7044-1 - Genesis (Type: Oblivion Dealer)
C - Released | A-8189-1 - Calamari (Type: Unknown) [Type: Kraken]
My current assumption on anomaly IDs are as follows:
Each anomaly ID contains three distinct parts. The classification number (A-xxxx-x), the Case, and the Type.
The classification number also has three parts:
The A, which is just Anomaly
The time in which the Institute discovered them in comparison to every other anomaly (For example, on this list, 'Local God - Animal' is the 27th anomaly in the Institute's database overall, and the 27th they ever made a file on. Similarly, the Oblivion Dealer is the 7044th, etc.)
The number of anomalies discovered by the local branch at the time of the report (Darkwick has 62 Local God - Animals on file, and 1 Oblivion Dealer, etc)
The case is simply 'What were they investigating when they found this anomaly?' or 'What was the original investigation for?' or something along those lines.
Pulling a few examples of this:
The Father Farm investigation was about why the employees were all suddenly quitting, and later an investigation on why the wishes were granted. The original intent, employees quitting, was caused by the Cat. When they ascertained the cat wasn't working alone, they investigated the other suspicion.
Therefore, despite the anomalies being in the same area and episode and working together, the Cat is listed as Father Farm Cat, and the God is listed as Sheepdog.
This also applies to the Kyklos and Flower Witch. The original Kyklos investigation was related to Kisaragi Station, hence why hers is listed under that, while the Flower Witch was her own, separate investigation.
Origin is therefore an anomaly whose investigation was directly related to that particular anomaly. I... honestly can't explain Genesis, but I believe it might be that the investigation was related to its creation...? Shrugs.
And finally, the type is self explanatory. What kind of anomaly is it?