{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:7Y3R37MPFQYN4GSAVNNMEGBPQ7","short_pith_number":"pith:7Y3R37MP","canonical_record":{"source":{"id":"2502.08583","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-02-12T17:14:38Z","cross_cats_sorted":[],"title_canon_sha256":"69f003ba12593b10ccbe8c3c0e2fe3211f67408ab153b0db6d5c464e92868542","abstract_canon_sha256":"ae76dee8981a4da5b6f05f07a7312729b9ebaaeaa5ba101ba6411913465dd608"},"schema_version":"1.0"},"canonical_sha256":"fe371dfd8f2c30de1a40ab5ac2182f87d815ba4bf6b21c36921cf48cd2736043","source":{"kind":"arxiv","id":"2502.08583","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.08583","created_at":"2026-07-05T10:51:05Z"},{"alias_kind":"arxiv_version","alias_value":"2502.08583v2","created_at":"2026-07-05T10:51:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.08583","created_at":"2026-07-05T10:51:05Z"},{"alias_kind":"pith_short_12","alias_value":"7Y3R37MPFQYN","created_at":"2026-07-05T10:51:05Z"},{"alias_kind":"pith_short_16","alias_value":"7Y3R37MPFQYN4GSA","created_at":"2026-07-05T10:51:05Z"},{"alias_kind":"pith_short_8","alias_value":"7Y3R37MP","created_at":"2026-07-05T10:51:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:7Y3R37MPFQYN4GSAVNNMEGBPQ7","target":"record","payload":{"canonical_record":{"source":{"id":"2502.08583","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-02-12T17:14:38Z","cross_cats_sorted":[],"title_canon_sha256":"69f003ba12593b10ccbe8c3c0e2fe3211f67408ab153b0db6d5c464e92868542","abstract_canon_sha256":"ae76dee8981a4da5b6f05f07a7312729b9ebaaeaa5ba101ba6411913465dd608"},"schema_version":"1.0"},"canonical_sha256":"fe371dfd8f2c30de1a40ab5ac2182f87d815ba4bf6b21c36921cf48cd2736043","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:51:05.308401Z","signature_b64":"Rlgztd/YFmttRR631OoLwxOBcS6VSb6TU7u4np5ZYzVoJtbOJj4sl1Bgv59Mk7deDPGB6ItcjEGGS7bZOGtCAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe371dfd8f2c30de1a40ab5ac2182f87d815ba4bf6b21c36921cf48cd2736043","last_reissued_at":"2026-07-05T10:51:05.307851Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:51:05.307851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.08583","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:51:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X+o9jZBUQJBaqddD0VhpH1/WA9NSk22hG04oiQCdIhQc0+sPypGX0BN2a3EFTlA+3ciGVPVdAhkkWFKLqIVmCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-27T09:45:44.624070Z"},"content_sha256":"b866c2330f611a888f615f66b86876825b822765da2cfb47d839c0d8e0548931","schema_version":"1.0","event_id":"sha256:b866c2330f611a888f615f66b86876825b822765da2cfb47d839c0d8e0548931"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:7Y3R37MPFQYN4GSAVNNMEGBPQ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Lazar Radi\\v{c}evi\\'c, Matteo Verzobio, Stevan Gajovi\\'c","submitted_at":"2025-02-12T17:14:38Z","abstract_excerpt":"We determine the probability that a random Weierstrass equation with coefficients in the $p$-adic integers defines an elliptic curve with a non-trivial $3$-torsion point, or with a degree $3$ isogeny, defined over the field of $p$-adic numbers. We determine these densities by calculating the corresponding $p$-adic volume integrals and analyzing certain modular curves. Additionally, we explore the case of $\\ell$-torsion for $\\ell>3$ prime."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.08583","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.08583/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:51:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WgobGHV2zpIVcQObQOQOb8F/nDioXwCbFpsFxYVs+4+VxXEwcrp/6UkkckY9AZUasugXBS6rD/HzHIZ75VpjBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-27T09:45:44.624464Z"},"content_sha256":"818492da54ea1b520d4f35d3054e40f3d45694248b1f3c61aa325c6faea29c15","schema_version":"1.0","event_id":"sha256:818492da54ea1b520d4f35d3054e40f3d45694248b1f3c61aa325c6faea29c15"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7Y3R37MPFQYN4GSAVNNMEGBPQ7/bundle.json","state_url":"https://pith.science/pith/7Y3R37MPFQYN4GSAVNNMEGBPQ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7Y3R37MPFQYN4GSAVNNMEGBPQ7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-07-27T09:45:44Z","links":{"resolver":"https://pith.science/pith/7Y3R37MPFQYN4GSAVNNMEGBPQ7","bundle":"https://pith.science/pith/7Y3R37MPFQYN4GSAVNNMEGBPQ7/bundle.json","state":"https://pith.science/pith/7Y3R37MPFQYN4GSAVNNMEGBPQ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7Y3R37MPFQYN4GSAVNNMEGBPQ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:7Y3R37MPFQYN4GSAVNNMEGBPQ7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ae76dee8981a4da5b6f05f07a7312729b9ebaaeaa5ba101ba6411913465dd608","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-02-12T17:14:38Z","title_canon_sha256":"69f003ba12593b10ccbe8c3c0e2fe3211f67408ab153b0db6d5c464e92868542"},"schema_version":"1.0","source":{"id":"2502.08583","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.08583","created_at":"2026-07-05T10:51:05Z"},{"alias_kind":"arxiv_version","alias_value":"2502.08583v2","created_at":"2026-07-05T10:51:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.08583","created_at":"2026-07-05T10:51:05Z"},{"alias_kind":"pith_short_12","alias_value":"7Y3R37MPFQYN","created_at":"2026-07-05T10:51:05Z"},{"alias_kind":"pith_short_16","alias_value":"7Y3R37MPFQYN4GSA","created_at":"2026-07-05T10:51:05Z"},{"alias_kind":"pith_short_8","alias_value":"7Y3R37MP","created_at":"2026-07-05T10:51:05Z"}],"graph_snapshots":[{"event_id":"sha256:818492da54ea1b520d4f35d3054e40f3d45694248b1f3c61aa325c6faea29c15","target":"graph","created_at":"2026-07-05T10:51:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2502.08583/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We determine the probability that a random Weierstrass equation with coefficients in the $p$-adic integers defines an elliptic curve with a non-trivial $3$-torsion point, or with a degree $3$ isogeny, defined over the field of $p$-adic numbers. We determine these densities by calculating the corresponding $p$-adic volume integrals and analyzing certain modular curves. Additionally, we explore the case of $\\ell$-torsion for $\\ell>3$ prime.","authors_text":"Lazar Radi\\v{c}evi\\'c, Matteo Verzobio, Stevan Gajovi\\'c","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-02-12T17:14:38Z","title":"The density of elliptic curves over $\\mathbb{Q}_p$ with a rational 3-torsion point or a rational 3-isogeny"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.08583","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b866c2330f611a888f615f66b86876825b822765da2cfb47d839c0d8e0548931","target":"record","created_at":"2026-07-05T10:51:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ae76dee8981a4da5b6f05f07a7312729b9ebaaeaa5ba101ba6411913465dd608","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-02-12T17:14:38Z","title_canon_sha256":"69f003ba12593b10ccbe8c3c0e2fe3211f67408ab153b0db6d5c464e92868542"},"schema_version":"1.0","source":{"id":"2502.08583","kind":"arxiv","version":2}},"canonical_sha256":"fe371dfd8f2c30de1a40ab5ac2182f87d815ba4bf6b21c36921cf48cd2736043","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe371dfd8f2c30de1a40ab5ac2182f87d815ba4bf6b21c36921cf48cd2736043","first_computed_at":"2026-07-05T10:51:05.307851Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:51:05.307851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rlgztd/YFmttRR631OoLwxOBcS6VSb6TU7u4np5ZYzVoJtbOJj4sl1Bgv59Mk7deDPGB6ItcjEGGS7bZOGtCAw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:51:05.308401Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.08583","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b866c2330f611a888f615f66b86876825b822765da2cfb47d839c0d8e0548931","sha256:818492da54ea1b520d4f35d3054e40f3d45694248b1f3c61aa325c6faea29c15"],"state_sha256":"30b1f991c5acf013ef1394d7b3f8d0058756f8a445e746c9c9a96e17ef76aaf1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WgitYUQFKN07BdhY1XfMus7wagtTU4JdCqca8h5AFCABnSfvdABwiqkOFVbb9XO/TpGfwaRbayrKvGN16sl6AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-27T09:45:44.627069Z","bundle_sha256":"75d3be4bc2c65dcc638ff6b9bfd89b56ef23f377da146517363f26ad7826f83f"}}