{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:HA5R37P7AAAOVWMBLBCKQ7KI6X","short_pith_number":"pith:HA5R37P7","canonical_record":{"source":{"id":"math/0612670","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2006-12-21T20:55:59Z","cross_cats_sorted":[],"title_canon_sha256":"4f83062ea3157de1ad582a47e86513e8b5ab8cf86673b001a46295a0a7caa65e","abstract_canon_sha256":"30a21a0aec6612cc8ac3db1b82db33fce36ed2871de803d60ff17f8ca29f581d"},"schema_version":"1.0"},"canonical_sha256":"383b1dfdff0000ead9815844a87d48f5d8b9ca14d23b80e4a6daf78ffaba120d","source":{"kind":"arxiv","id":"math/0612670","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612670","created_at":"2026-05-18T00:19:48Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612670v1","created_at":"2026-05-18T00:19:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612670","created_at":"2026-05-18T00:19:48Z"},{"alias_kind":"pith_short_12","alias_value":"HA5R37P7AAAO","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"HA5R37P7AAAOVWMB","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"HA5R37P7","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:HA5R37P7AAAOVWMBLBCKQ7KI6X","target":"record","payload":{"canonical_record":{"source":{"id":"math/0612670","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2006-12-21T20:55:59Z","cross_cats_sorted":[],"title_canon_sha256":"4f83062ea3157de1ad582a47e86513e8b5ab8cf86673b001a46295a0a7caa65e","abstract_canon_sha256":"30a21a0aec6612cc8ac3db1b82db33fce36ed2871de803d60ff17f8ca29f581d"},"schema_version":"1.0"},"canonical_sha256":"383b1dfdff0000ead9815844a87d48f5d8b9ca14d23b80e4a6daf78ffaba120d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:48.191863Z","signature_b64":"3rSiaQsMeGwNcdhyfCp4Bz8HL51IkbJP5Zh2ai5sgsl0Q6zeIUbYzmILrtAP1kU6EUuBIhQKXGsLuoB863J7BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"383b1dfdff0000ead9815844a87d48f5d8b9ca14d23b80e4a6daf78ffaba120d","last_reissued_at":"2026-05-18T00:19:48.191108Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:48.191108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0612670","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:19:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Szb3TSB5+N/HXANCEB+FyrJcbc/khnsVy+Q8WrCjGHx9xKmUVvxn92vlZ56Dni1Fbvq78uRz72amiStgtuBQAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T10:10:45.477036Z"},"content_sha256":"5fedae4f0e365a81663492b046069b9f6f862ac2365aae41ccf37c78162b7059","schema_version":"1.0","event_id":"sha256:5fedae4f0e365a81663492b046069b9f6f862ac2365aae41ccf37c78162b7059"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:HA5R37P7AAAOVWMBLBCKQ7KI6X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Identities between Mahler measures","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fernando Rodriguez Villegas","submitted_at":"2006-12-21T20:55:59Z","abstract_excerpt":"The purpose of this short note is to give a proof of the following identity between (logarithmic) Mahler measures m(y^2+2xy+y-x^3-2x^2-x)=5/7*m(y^2+4xy+y-x^3+x^2) which is one of many examples that arise from the comparison of Mahler measures and special values of L-functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612670","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:19:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N6d4+VKn5rNM0M06QXBmxXTS3Pygf1q5dL/r6cczHbAPlMmU8shb21hgtCg2uae5ItYpgbu3UvViOoK1roxZDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T10:10:45.477392Z"},"content_sha256":"60aadd0948f651a2fae7e2f6b95744c33a5420b7b9c4a942ef073083ecd71433","schema_version":"1.0","event_id":"sha256:60aadd0948f651a2fae7e2f6b95744c33a5420b7b9c4a942ef073083ecd71433"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HA5R37P7AAAOVWMBLBCKQ7KI6X/bundle.json","state_url":"https://pith.science/pith/HA5R37P7AAAOVWMBLBCKQ7KI6X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HA5R37P7AAAOVWMBLBCKQ7KI6X/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":"2026-06-12T10:10:45Z","links":{"resolver":"https://pith.science/pith/HA5R37P7AAAOVWMBLBCKQ7KI6X","bundle":"https://pith.science/pith/HA5R37P7AAAOVWMBLBCKQ7KI6X/bundle.json","state":"https://pith.science/pith/HA5R37P7AAAOVWMBLBCKQ7KI6X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HA5R37P7AAAOVWMBLBCKQ7KI6X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:HA5R37P7AAAOVWMBLBCKQ7KI6X","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":"30a21a0aec6612cc8ac3db1b82db33fce36ed2871de803d60ff17f8ca29f581d","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2006-12-21T20:55:59Z","title_canon_sha256":"4f83062ea3157de1ad582a47e86513e8b5ab8cf86673b001a46295a0a7caa65e"},"schema_version":"1.0","source":{"id":"math/0612670","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612670","created_at":"2026-05-18T00:19:48Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612670v1","created_at":"2026-05-18T00:19:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612670","created_at":"2026-05-18T00:19:48Z"},{"alias_kind":"pith_short_12","alias_value":"HA5R37P7AAAO","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"HA5R37P7AAAOVWMB","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"HA5R37P7","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:60aadd0948f651a2fae7e2f6b95744c33a5420b7b9c4a942ef073083ecd71433","target":"graph","created_at":"2026-05-18T00:19:48Z","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"},"paper":{"abstract_excerpt":"The purpose of this short note is to give a proof of the following identity between (logarithmic) Mahler measures m(y^2+2xy+y-x^3-2x^2-x)=5/7*m(y^2+4xy+y-x^3+x^2) which is one of many examples that arise from the comparison of Mahler measures and special values of L-functions.","authors_text":"Fernando Rodriguez Villegas","cross_cats":[],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2006-12-21T20:55:59Z","title":"Identities between Mahler measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612670","kind":"arxiv","version":1},"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":"sha256:5fedae4f0e365a81663492b046069b9f6f862ac2365aae41ccf37c78162b7059","target":"record","created_at":"2026-05-18T00:19:48Z","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":"30a21a0aec6612cc8ac3db1b82db33fce36ed2871de803d60ff17f8ca29f581d","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2006-12-21T20:55:59Z","title_canon_sha256":"4f83062ea3157de1ad582a47e86513e8b5ab8cf86673b001a46295a0a7caa65e"},"schema_version":"1.0","source":{"id":"math/0612670","kind":"arxiv","version":1}},"canonical_sha256":"383b1dfdff0000ead9815844a87d48f5d8b9ca14d23b80e4a6daf78ffaba120d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"383b1dfdff0000ead9815844a87d48f5d8b9ca14d23b80e4a6daf78ffaba120d","first_computed_at":"2026-05-18T00:19:48.191108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:48.191108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3rSiaQsMeGwNcdhyfCp4Bz8HL51IkbJP5Zh2ai5sgsl0Q6zeIUbYzmILrtAP1kU6EUuBIhQKXGsLuoB863J7BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:48.191863Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0612670","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5fedae4f0e365a81663492b046069b9f6f862ac2365aae41ccf37c78162b7059","sha256:60aadd0948f651a2fae7e2f6b95744c33a5420b7b9c4a942ef073083ecd71433"],"state_sha256":"8e941df0295006a65196e8d376c61d2a0dd38609d791e6ec7d9086d0d65cceda"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b8sxVhCewd+THsiA6N8qGKDEzskxHUKotkewjQgMCoyb5gAYA9nBUyj/9t2aSV0oEg3GvvrNcPDdrLEhwnrIDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T10:10:45.479455Z","bundle_sha256":"1fbde72a70e7879c62147c2bf79a4d3532d910aa7e5de50cc5d9158317c07b1a"}}